Leeson's equation

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Leeson's equation is an empirical expression that describes an oscillator's phase noise spectrum.

Leeson's expression[1] for single-sideband (SSB) phase noise in dBc/Hz (decibels relative to output level per Hertz) and augmented for flicker noise:[2]

where f0 is the output frequency, Ql is the loaded Q, fm is the offset from the output frequency (Hz), fc is the 1/f corner frequency, F is the noise factor of the amplifier, k is Boltzmann's constant in Joules/Kevin, T is absolute temperature in Kelvins, and Ps is the output power.[3]


  1. ^ Leeson, D. B. (February 1966), "A Simple Model of Feedback Oscillator Noise Spectrum", Proceedings of the IEEE, 54 (2): 329–330, doi:10.1109/PROC.1966.4682 
  2. ^ Rhea, Randall W. (1997), Oscillator Design & Computer Simulation (Second ed.), McGraw-Hill, ISBN 0-07-052415-7 , p. 115.
  3. ^ Zumbahlen, Hank; Analog Devices, Inc. (2011-08-30). Zumbahlen, Hank, ed. Linear Circuit Design Handbook. Newnes. ISBN 9780080559155. 

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